I would be inclined to say the final result is 1d3+1 cold + 1d3 piercing (2d3+1 total).
While the rules don't explicitly say that they add the 1d3+1, they also don't explicitly say that they replace it.
The rules for alchemical components read as such:
An alchemical power component is an alchemical item used as a material component or focus for a spell in order to alter or augment the spell's normal effects. What follows is a sample of these effects using this item as a component; your GM may allow other combinations.
So from this we know 100% that it's altering/augmenting the original spell. It's worth noting that it's not explicitly replacing.
Of course, some alchemical components do explicitly say they replace the effect of the original spell. For example, see the rules text for using Smokestick as a material component for Obscuring Mist:
Obscuring Mist (M): The spell creates a smoky haze instead of mist. This haze cannot be dispersed by fire spells and dissipates naturally after 1 minute.
We can clearly see here that it says the spell creates the smoky haze instead of mist. That's pretty clear.
On the other hand, let's look at the rules for using Liquid Ice as a material component for Ray of Frost:
Ray of Frost (M): The spell creates an icicle of frozen water vapor that strikes the target and deals 1d3 points of piercing damage and 1 point of cold damage.
There is absolutely zero mention here of "replace", "instead", or anything of that sort. Given all of the above, I'm inclined to say that the 1d3+1 is in addition to, and not in place of the normal spell effect.